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Hemisphere Volume Calculator

Calculate the volume of a hemisphere using radius with our hemisphere volume calculator. Get the hemisphere formula, steps, and instant results.

r = 5 cm
pi setting: pi = 3.14159265
pi Precision:
Hemisphere Volume
261.7994cm³
Decimals:
Step-by-Step Mathematical Solution
Formula:V = (2/3) × π × r³
Steps:
1.Input Radius (r) = 5 cm
2.Formula: V = (2/3) × π × r³
3.Cube the radius: r³ = 5³ = 125
4.Multiply by π: π × r³ = 3.14159265 × 125 = 392.6991
5.Multiply by 2/3: V = (2/3) × π × r³ = 261.7994 cm³
Calculated Volume:261.7994 cm³

What Is a Hemisphere?

A hemisphere is exactly one-half of a sphere cut by a plane through its center. It has one curved surface and one flat circular base.

Common examples of hemispheres include domes, bowl-like covers, half-ball molds, and rounded tanks split into two equal parts.

Volume of a Hemisphere Formula

Standard Formula
V = (2/3) × π × r³

Formula Variables Explained:

rRadius

The distance from the center of the flat circular face to the outer curved edge of the hemisphere.

πPi

The mathematical constant approximately equal to 3.14159265.

A hemisphere has half the volume of a full sphere. Since a sphere volume is V = (4/3) × π × r³, the hemisphere volume becomes V = (2/3) × π × r³.

How to find the volume of a Hemisphere?

  1. 1Measure the hemisphere radius (r).
  2. 2Cube the radius: r³ = r × r × r.
  3. 3Multiply by π.
  4. 4Multiply the result by 2/3.
  5. 5Write the final answer in cubic units such as cm³, m³, in³, or ft³.

Example: Calculate the Volume of a Hemisphere

Example 1: Find the volume of a hemisphere with radius 6 cm

Problem: A dome-shaped bowl has a radius of 6 cm. Calculate the volume it can hold.

Solution Steps:
  • Formula: V = (2/3) × π × r³
  • Substitute r = 6: V = (2/3) × π × 6³
  • Calculate 6³ = 216
  • V = (2/3) × π × 216
  • V = 144π
  • V is approximately 452.39 cm³
Final Volume:452.39 cm³ (or 144π cm³)

Example 2: Calculate hemisphere volume with radius 10 inches

Problem: A half-sphere mold has a radius of 10 inches. Find its enclosed volume.

Solution Steps:
  • Formula: V = (2/3) × π × r³
  • Substitute r = 10: V = (2/3) × π × 10³
  • Calculate 10³ = 1000
  • V = (2/3) × π × 1000
  • V is approximately 2094.40 in³
Final Volume:2094.40 cubic inches

Frequently Asked Questions (FAQ)

Q: Is hemisphere volume exactly half of sphere volume?

Yes. A hemisphere is one-half of a sphere, so its volume is exactly half of the sphere volume formula.

Q: Do I need the diameter to calculate hemisphere volume?

No. Radius alone is enough. If you only know the diameter, divide it by 2 first to get the radius.

Q: What units should the hemisphere volume result use?

Use cubic units that match your input length unit, such as cm³ for centimeters, m³ for meters, or ft³ for feet.

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